Title

Sub-Title

The parameters of duals of algebraic geometric codes on surfaces

Speaker:
Dr. Alain Couvreur
, INRIA.

abstract

It is well-known in the theory of codes on curves that the dual of an
algebraic-geometric code on a curve is an algebraic-geometric code on
the same curve. It turns out that this property does not hold in general
when the curve is replaced by an higher dimensional variety. This
observation motivates the study of this new class of codes which are the
duals of algebraic geometric codes on higher-dimensional varieties.

In this talk, after a brief review on the classical properties of codes
on curves, we will focus on the problem of finding the parameters of
duals of codes on surfaces. A method yielding a lower bound for the
minimum distance of such codes will be presented. This method, based on
the use of differential 2-forms and intersection theory on surfaces,
turns to be efficient provided the Picard Number of the surface is
small.